Remarks on an arbitrage-free condition for XVA

Abstract

After the financial crisis, it has been widely recognized that counterparty default risks have serious consequences and that there are remarkably large differences in various interest rates. As a result, the methodology for pricing derivative securities has been modified: Currently, the price of a derivative security is expressed as the so-called XVA, which is the risk-neutral price plus total valuation adjustment. In this paper, we aim to provide a theoretical interpretation of XVA: Some valuation adjustments are interpreted as the ``$0$th-order'' approximation of XVA. Further, we describe a sufficient condition to ensure the arbitrage-free property of the $0$th-order price approximation.